Simpleness and closedness of circles in compact Hermitian symmetric spaces
Simpleness and closedness of circles in compact Hermitian symmetric spaces
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紧埃尔米特对称空间中圆的简单性和封闭性
DOI：
10.21099/tkbjm/1496164041
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发表时间：
2000
影响因子：
0.7
通讯作者：
S. Udagawa
中科院分区：
文献类型：
--
作者：
T. Adachi;S. Maeda;S. Udagawa
本文首先用李代数理论形式主义解释了黎曼对称空间中的圆。特别地，它是一阶常微分方程组的解.我们把圆分成三种类型，并在紧Hermite对称空间中研究了这类圆的封闭性和简单性.因此，我们发现了许多开全纯圈和非单圈，注意在秩为1的紧致黎曼对称空间中不存在非单圈和开全纯圈。
We firstinterpret circlesin Riemannian Symmetric space by Lie algebro-theoreticformalism. In particular,itis a solution of the system of ordinary differentialequation of firstorder.We divide circlesinto 3-types.We investigateclosedness and simpleness forsuch circlesin compact Hermitian symmetric spaces. Consequently, we find many open holomorphic circlesand non-simple circles.Note that there exist no non-simple circlesand no open holomorphic circlesin compact Riemannian symmetric space of rank one.